Advertisements
Advertisements
प्रश्न
A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 300 μC. When potential across the capacitor is reduced by 100 V, the charge stored in it becomes 100 μC. Calculate The potential V and the unknown capacitance. What will be the charge stored in the capacitor if the voltage applied had increased by 100 V?
Advertisements
उत्तर
(i) Initial voltage, V1 = V volts, Charge stored,Q1 = 300 µC
Q1 = CV1 ..(1)
Changed potential, V2 = V-100 V
Q2 = 100 µC
Q2 = CV2 ..(2)
By dividing (2) from (1), we get `(Q_1)/(Q_2) = (CV_1)/(CV_2) => Q_1/Q_2 = V_1 /V_2`
`=> 300/100 = V/(V- 100) => V = 150 \text { volts }`
`∴ C = Q_1/V_1 = (300 xx 10^-6)/150 = 2 xx 10^-6 F = 2 μ F`
(ii) If the voltage applied had increased by 120 V, then V3 = 150+100 = 250 V
Hence, charge stored in the capacitor, Q3 = CV3 = 2×10-6×250 = 500 µC
(ii) If the voltage applied had increased by 120 V, then V3 = 150+100 = 250 V
Hence, charge stored in the capacitor, Q3 = CV3 = 2×10-6×250 = 500 µC
APPEARS IN
संबंधित प्रश्न
A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure . The width of each stair is a and the height is b. Find the capacitance of the assembly.
A cylindrical capacitor is constructed using two coaxial cylinders of the same length 10 cm and of radii 2 mm and 4 mm. (a) Calculate the capacitance. (b) Another capacitor of the same length is constructed with cylinders of radii 4 mm and 8 mm. Calculate the capacitance.
Find the equivalent capacitance of the infinite ladder shown in figure between the points A and B.
A capacitor of capacitance 2⋅0 µF is charged to a potential difference of 12 V. It is then connected to an uncharged capacitor of capacitance 4⋅0 µF as shown in figure . Find (a) the charge on each of the two capacitors after the connection, (b) the electrostatic energy stored in each of the two capacitors and (c) the heat produced during the charge transfer from one capacitor to the other.
The separation between the plates of a parallel-plate capacitor is 0⋅500 cm and its plate area is 100 cm2. A 0⋅400 cm thick metal plate is inserted into the gap with its faces parallel to the plates. Show that the capacitance of the assembly is independent of the position of the metal plate within the gap and find its value.
Consider the situation shown in figure. The plates of the capacitor have plate area A and are clamped in the laboratory. The dielectric slab is released from rest with a length a inside the capacitor. Neglecting any effect of friction or gravity, show that the slab will execute periodic motion and find its time period.
Capacitors P and Q have identical cross-sectional areas A and separation d. The space between the capacitors is filled with a dielectric of dielectric constant Er as shown in the figure. Calculate the capacitance of capacitors P and Q.
The radius of a sphere of capacity 1 microfarad in the air is ______
Two similar conducting spheres having charge+ q and -q are placed at 'd' seperation from each other in air. The radius of each ball is r and the separation between their centre is d (d >> r). Calculate the capacitance of the two ball system ______.
